{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial 1b - Determining Lens Properties"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "nbsphinx-toctree"
    ]
   },
   "source": [
    "### May 2024"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This tutorial describes how to retrieve common optical properties from a lens in Optiland, including:\n",
    "\n",
    "- Front and back focal length\n",
    "- Front and back, principle, focal, and nodal plane locations\n",
    "- Aperture information, such as F-Number, entrance or exit pupil diameter, etc.\n",
    "- Locations of entrance/exit pupils\n",
    "- Optical invariant\n",
    "- Marginal/chief rays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from optiland.samples.objectives import CookeTriplet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "lens = CookeTriplet()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lens.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Front focal length: -50.0 mm\n",
      "Focal length: 50.0 mm\n",
      "Front focal point: -37.3 mm\n",
      "Back focal point: 0.2 mm\n",
      "Front principal plane: 12.7 mm\n",
      "Back principal plane: -49.8 mm\n",
      "Front nodal plane: 12.7 mm\n",
      "Back nodal plane: -49.8 mm\n"
     ]
    }
   ],
   "source": [
    "print(f\"Front focal length: {lens.paraxial.f1():.1f} mm\")\n",
    "print(f\"Focal length: {lens.paraxial.f2():.1f} mm\")\n",
    "print(f\"Front focal point: {lens.paraxial.F1():.1f} mm\")\n",
    "print(f\"Back focal point: {lens.paraxial.F2():.1f} mm\")\n",
    "print(f\"Front principal plane: {lens.paraxial.P1():.1f} mm\")\n",
    "print(f\"Back principal plane: {lens.paraxial.P2():.1f} mm\")\n",
    "print(f\"Front nodal plane: {lens.paraxial.N1():.1f} mm\")\n",
    "print(f\"Back nodal plane: {lens.paraxial.N2():.1f} mm\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Regarding cardinal points, Optiland defines object space quantities relative to the first lens surface (index 1) and image space quantities relative to the image surface."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Entrance pupil diameter: 10.0 mm\n",
      "Exit pupil diameter: 10.2 mm\n"
     ]
    }
   ],
   "source": [
    "print(f\"Entrance pupil diameter: {lens.paraxial.EPD():.1f} mm\")\n",
    "print(f\"Exit pupil diameter: {lens.paraxial.XPD():.1f} mm\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Entrance pupil position: 11.5 mm\n",
      "Exit pupil position: -51.0 mm\n"
     ]
    }
   ],
   "source": [
    "print(f\"Entrance pupil position: {lens.paraxial.EPL():.1f} mm\")\n",
    "print(f\"Exit pupil position: {lens.paraxial.XPL():.1f} mm\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Magnification is generally computed for finite objects and not for systems like the one we're analyzing here. We compute it only as an illustration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Image-space F-Number: 5.0\n",
      "Magnification: -0.0\n",
      "Invariant: -1.820\n"
     ]
    }
   ],
   "source": [
    "print(f\"Image-space F-Number: {lens.paraxial.FNO():.1f}\")\n",
    "print(f\"Magnification: {lens.paraxial.magnification():.1f}\")\n",
    "print(f\"Invariant: {lens.paraxial.invariant():.3f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Marginal Ray: \n",
      "\tSurface 0: y = 5.000, u = 0.000\n",
      "\tSurface 1: y = 5.000, u = -0.087\n",
      "\tSurface 2: y = 4.716, u = -0.148\n",
      "\tSurface 3: y = 3.826, u = -0.025\n",
      "\tSurface 4: y = 3.801, u = 0.076\n",
      "\tSurface 5: y = 4.162, u = 0.027\n",
      "\tSurface 6: y = 4.242, u = -0.100\n",
      "\tSurface 7: y = 0.021, u = -0.100\n"
     ]
    }
   ],
   "source": [
    "print(\"Marginal Ray: \")\n",
    "\n",
    "ya, ua = lens.paraxial.marginal_ray()\n",
    "for k in range(len(ya)):\n",
    "    print(f\"\\tSurface {k}: y = {ya[k, 0]:.3f}, u = {ua[k, 0]:.3f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Chief Ray: \n",
      "\tSurface 0: y = -4.190, u = 0.364\n",
      "\tSurface 1: y = -4.190, u = 0.297\n",
      "\tSurface 2: y = -3.221, u = 0.487\n",
      "\tSurface 3: y = -0.295, u = 0.295\n",
      "\tSurface 4: y = -0.000, u = 0.479\n",
      "\tSurface 5: y = 2.275, u = 0.284\n",
      "\tSurface 6: y = 3.113, u = 0.356\n",
      "\tSurface 7: y = 18.125, u = 0.356\n"
     ]
    }
   ],
   "source": [
    "print(\"Chief Ray: \")\n",
    "\n",
    "yb, ub = lens.paraxial.chief_ray()\n",
    "for k in range(len(yb)):\n",
    "    print(f\"\\tSurface {k}: y = {yb[k, 0]:.3f}, u = {ub[k, 0]:.3f}\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
